Bug in Maxima interface wrt polylog

[rwst]

sage: bool(x*polylog(x,x)==0)
...
/home/ralf/sage/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.pyc in composition(self, ex, operator)
    644         #FIXME: consider stripping pyobjects() in ops
    645         if hasattr(operator, self.name_init + "evaled_"):
--> 646             return getattr(operator, self.name_init + "evaled_")(*ops)
    647         else:
    648             ops = [self(_) for _ in ops]

/home/ralf/sage/local/lib/python2.7/site-packages/sage/functions/log.pyc in _maxima_init_evaled_(self, *args)
    451 
    452         n, x = args_maxima
--> 453         if int(n) in [1,2,3]:
    454             return 'li[%s](%s)'%(n, x)
    455         else:

ValueError: invalid literal for int() with base 10: '_SAGE_VAR_x'

Component: symbolics

Author: Frédéric Chapoton

Branch/Commit: 8f4f726

Reviewer: Dave Morris

Issue created by migration from https://trac.sagemath.org/ticket/21907

[fchapoton]

comment:1

This seems to be invalid. polylog(x,x) is not correct, the first argument must be an integer.

Of course, one could ask for a better error message.

https://doc.sagemath.org/html/en/reference/functions/sage/functions/log.html?#sage.functions.log.Function_polylog

[DaveWitteMorris]

comment:2

I don't understand. The documentation seems to clearly state that non-integral values are allowed:

This definition is valid for arbitrary complex order s and for all complex 
arguments z with |z|<1; it can be extended to |z|≥1 by the process of analytic 
continuation.

And non-integral values are accepted in my testing:

sage: polylog(1.1 + 2.2*I, 3.3 + 4.4*I)                                                        
-13.9758786469542 + 8.16803654165145*I

PS I think the documentation should tell us which parameter is s and which is z. (And I find the phrase "complex order s" to be confusing.)

[fchapoton]

comment:3

This seems to work fine in 9.3.beta6, for some reason.

[fchapoton]

comment:4

Here is a branch adding a doctest, and cleaning the file "en passant".

---

New commits:

88acb4c

cleanup the log file, plus one doctest for polylog

[fchapoton]

Branch: u/chapoton/21907

[fchapoton]

Commit: 88acb4c

[fchapoton]

Author: Frédéric Chapoton